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AVOID ERRORS
Choice D gives the
number of long sleeve
T-shirts, but the
question asks for the
number of short sleeve
T-shirts. So you still
need to solve for x in
Step 3.
162 Chapter 3 Linear Systems and Matrices
E XAMPLE 3 TAKS PRACTICE: Multiple Choice
To raise money for new football uniforms, your school sells silk-screened
T-shirts. Short sleeve T-shirts cost the school $8 each and are sold for $11
each. Long sleeve T-shirts cost the school $10 each and are sold for $16 each.
The school spends a total of $3900 on T-shirts and sells all of them for $5925.
How many of the short sleeve T-shirts are sold?
A 75 B 150 C 175 D 250
Solution
STEP 1 Write verbal models for this situation.
Equation 1
Short sleeve
cost
(dollars/shirt)
Equation 2
p
Short sleeve
shirts
(shirts)
1
Long sleeve
cost
(dollars/shirt)
p
Long sleeve
shirts
(shirts)
5
Total
cost
(dollars)
8 p x 1 10 p y 5 3900
Short sleeve
selling price
(dollars/shirt)
p
Short sleeve
shirts
(shirts)
1
Long sleeve
selling price
(dollars/shirt)
p
Long sleeve
shirts
(shirts)
5
Total
revenue
(dollars)
11 p x 1 16 p y 5 5925
STEP 2 Write a system of equations.
Equation 1 8x 1 10y 5 3900 Total cost for all T-shirts
Equation 2 11x 1 16y 5 5925 Total revenue from T-shirts sold
STEP 3 Solve the system using the elimination method.
Multiply Equation 1 by 211 and Equation 2 by 8 so that the
coefficients of x differ only in sign.
8x 1 10y 5 3900 3211 288x 2 110y 5242,900
11x 1 16y 5 5925 3 8
88x 1 128y 5 47,400
Add the revised equations and solve for y. 18y 5 4500
y 5 250
Substitute the value of y into one of the original equations
and solve for x.
8x 1 10y 5 3900 Write Equation 1.
8 x 1 10(250) 5 3900 Substitute 250 for y.
8x 1 2500 5 3900 Simplify.
x 5 175 Solve for x.
The school sold 175 short sleeve T-shirts and 250 long sleeve T-shirts.
c The correct answer is C. A B C D